You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 18% and a standard deviation of 21% and a Treasury bill with a rate of return of 4%. How much money should be invested in the risky asset to form a portfolio with an expected return of 13%?

The amount of money invested in risky asset = $6428.57

Explanation:

The portfolio return is made up of the returns of the individual returns of securities in a portfolio multiplied by their weight in the portfolio.

Thus the formula for portfolio retyurn is,

Portfolio return = wA * rA + wB * rB + ... + wX * rX and so on

Where,

w represents weight of security in portfolio r represents the return on that security

Plugging in the values in the formula,

let x be the weight of investment in risky asset

then x-1 is weight of investment in risk free asset

0.13 = x * 0.18 + (1-x) * 0.04

0.13 = 0.18x + 0.04 - 0.04x

0.13 - 0.04 = 0.14x

0.09 / 0.14 = x

x = 9/14 or 0.6429 or 64.29%

The amount of money invested in risky asset is 9/14 * 10000 = $6428.57